基于线性稳定性分析的翼尖涡摇摆机制

Mechanism of wingtip vortex wandering based on linear stability analysis

在涡不稳定性特征的影响下,翼尖涡会在尾迹中发生摇摆运动。为了揭示翼尖涡摇摆的本质原因以及发展机理,采用体视粒子图像测速(SPIV)技术和线性稳定性分析方法对不同雷诺数和迎角下NACA0015等直翼产生的翼尖涡在尾迹区的不稳定性特征及发展进行研究。结果表明:在1~6倍弦长的尾迹区内,翼尖涡存在摇摆现象,摇摆幅值随流向放大,且摇摆运动沿流向逐渐呈现出各向异性特征;在大迎角条件下,翼尖涡摇摆幅值随流向增长更快。采用线性稳定性分析方法,定量化分析翼尖涡的稳定性、空间/时间不稳定性放大率和扰动频率随流向的发展过程。结果显示,在雷诺数2.1×10^5~3.5×10^5范围内,翼尖涡均处于临界稳定状态,扰动频率为3~5Hz。基于线性稳定性分析结果,发现在大迎角条件下翼尖涡时间/空间不稳定性放大率更大,解释了当迎角增大时翼尖涡摇摆幅值随流向增长更快的现象。另外,由线性稳定性分析得到的最不稳定模态显示翼尖涡的横向速度扰动具有明显的方向性,从而诱导翼尖涡产生摇摆运动;速度扰动方向的周期性变化则使翼尖涡摇摆区别于一维的随机振荡,而是表现为在各方向均含有分量且具有主频的摇摆运动。这种由不稳定性导致的速度扰动是翼尖涡摇摆的内在机制,其不稳定性放大率控制着摇摆幅值的增长速率,而其横向速度扰动的方向性与周期性则决定了翼尖涡的摇摆特征。

Under the influence of vortex instability,wingtip vortex demonstrates a certain motion of wandering in its wake.To understand the mechanism and the evolution of vortex wandering,the instability and its development of the wingtip vortex generated by a NACA0015rectangular wing are investigated by conducting Stereo Particle Image Velocimetry(SPIV)experiments at different Reynolds numbers and angles of attack.The results show that vortex wandering exists in the wake of 1-6 chordlength and manifests anisotropy that gradually amplifies along its streamwise position.The amplitude of wandering grows faster with streamwise distance at larger angle of attack.Based on the experimental results,the amplification ratio of the spatial/temporal instability of wingtip vortex,frequency of perturbation,and their evolution along the streamwise direction are obtained through linear stability analysis.It is found that the wingtip vortex is marginally stable within Reynolds number= 2.1×10^5-3.5×10^5 with the perturbation frequency around 3-5Hz.The fact that wingtip vortex is more unstable at larger angle of attack,shown by larger spatial/temporal growth rate,causes faster development of disturbance,which further leads to a quicker growth of wandering amplitude along the streamwise direction.Meanwhile,the transverse velocity perturbation of the most unstable mode obtained by linear stability analysis reveals strong directionality,which shifts the vortex core and causes the wandering motion of wingtip vortex.Different from the one-dimensional random oscillation,the periodic variance of velocity perturbation forces wingtip vortex to wander in each direction with certain dominate frequency.This velocity perturbation fomented by instability is the mechanism causing vortex wandering.The amplification ratio of instability controls the growth rate of its amplitude,and the directionality and periodicity of velocity perturbation accounts for the feature of this motion.